Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x-2y &= -3 \\ -2x-y &= 6\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-y = 2x+6$ Divide both sides by $-1$ to isolate $y$ $y = {-2x - 6}$ Substitute this expression for $y$ in the first equation. $-7x-2({-2x - 6}) = -3$ $-7x + 4x + 12 = -3$ Simplify by combining terms, then solve for $x$ $-3x + 12 = -3$ $-3x = -15$ $x = 5$ Substitute $5$ for $x$ back into the top equation. $-7( 5)-2y = -3$ $-35-2y = -3$ $-2y = 32$ $y = -16$ The solution is $\enspace x = 5, \enspace y = -16$.